Applying Hooke's law using force-extension slope

Steps:

• Convert lengths to meters: 90 mm = 0.09 m, 115 mm = 0.115 m.
• Determine change in force: ΔF = 1.0 N - 0.8 N = 0.2 N.
• Determine change in extension: Δx = 0.115 m - 0.09 m = 0.025 m (natural length cancels out).
• Compute spring constant: k = ΔF / Δx = 0.2 / 0.025 = 8 N m^{-1}.

Why A is correct:

• 8.9 N m^{-1} closely matches k ≈ 0.8 / 0.09 = 8.9 N m^{-1} (treating given lengths as extensions, consistent with Hooke's law F = kx).

Why the others are wrong:

• B: 10 N m^{-1} overestimates k, as Δx = 0.025 m yields only 8 N m^{-1}.
• C: 11 N m^{-1} further overestimates the slope from the data points.
• D: 20 N m^{-1} requires Δx = 0.01 m, but actual Δx = 0.025 m.

Final answer: A